The invention is particularly applicable to transmitting data by radio in a form which may be considered as being analog whereas on reception the transmitted signal, transposed back to base band, must be processed digitally. The conversion of the transmitted analog signal into digital form then takes place by sampling and coding at a rate which is much higher than the Shannon rate required for the bandwidth of the signal being encoded. Such over-sampling makes it possible to use analog low-pass filters which are cheaper and simpler in design and which are required, in any case prior to analog-to-digital conversion. Nyquist filtering of the transmission channel may also be performed on an over-sampled signal, prior to decimation.
Decimation is an operation which consists in retaining only one sample out of R samples in a sequence of high rate samples of a digital input signal. R is the decimation ratio. Analysis shows that if R is too high relative to the spectrum of the input signal, then decimation gives rise to spectrum folding which ought to be avoided. To do this, it is common practice to shape the input signal prior to decimation. Shaping is done by low-pass type filtering which does not affect the signal to be retained after decimation.
The usual way of accomplishing such filtering on a digital signal is to use a finite impulse response (FIR) filter, in which each output sample is the sum of N prior samples of the input signal as weighted by appropriate coefficients. Such a filter performs N parallel multiplications whose results are delayed and summed. Multiplication is the more complex operation and the time required for the multiplication limits the maximum throughput of the filter. A filter implemented in a given technology thus has a limited field of application.
However, it is also known that an FIR filter may be replaced by a series combination of a prefilter and an equalizer. This is explained in the article "A new approach to FIR digital filters with fewer multipliers and reduced sensitivity" by J. W. Adams and A. N. Willson, published in IEEE Transactions on Circuits and Systems, Vol. CAS-30, pp. 277-283, May 1983. The prefilter is a simplified FIR filter comprising a small number of very simple coefficients (0,-1, 1, . . . ) so that it does not need to perform multiplications.
The maximum possible throughput of such a filter is limited solely by addition operations. This throughput is considerably higher than that of a conventional FIR filter. The equalizer is also an FIR filter and its function is to correct the transfer function of the prefilter and to ensure that the overall transfer function (prefilter plus equalizer) is as required. Since the equalizer provides only one correction, it is of relatively low order and therefore performs only a relatively small number of multiplications. When equipment is implemented in the form of very large scale integration (VLSI), this reduces the area occupied by the filter. The limitation on the maximum sampling rate acceptable by the filter is the same as for a conventional FIR filter.
As mentioned at the beginning of the present text, the invention relates particularly, but not exclusively, to cases where an oversampled signal is also to be filtered for transmission purposes (Nyquist filter). This filtering operation must necessarily be performed prior to decimation. It may, naturally, be combined with that described above which is specific to decimation. This gives rise to different coefficients and generally emphasizes problems relating to the limited maximum sampling rate in both modes of filtering mentioned above.
The present invention seeks to provide a solution to these problems in the form of an integrated decimation filter in which there are no portions that perform multiplication at the high rate at which the input signal is sampled.